Study of LY573636-sodium in Essential Thrombocythemia and Acute Myeloid Leukemia

Inclusion Criteria: * Participants who have a diagnosis of either essential thrombocythemia or acute myeloid leukemia that is relapsed or refractory to at least one prior standard treatment. If participants have acute promyelocytic leukemia, they must be resistant and/or intolerant of both all trans retinoic acid (ATRA) and arsenic trioxide. * Are at least 18 years of age. * Have given written informed consent approved by Lilly and the ethical review board (ERB)/institutional review board (IRB) governing the site. * Must have adequate hepatic and renal function. * Have discontinued all previous therapies for cancer, including chemotherapy, radiotherapy, immunotherapy, cancer-related hormonal therapy, or other investigational therapy for at least 21 days for myelosuppressive agents (such as cytarabine, daunorubicin, and gemtuzumab ozogamicin) or 14 days for non-myelosuppressive agents prior to receiving study drug and recovered from the acute effects of therapy. Hydroxyurea used to control peripheral blood blast count is permitted within these respective periods, but it must be stopped at least 24 hours before study drug administration. * Males and females with reproductive potential must agree to use medically approved contraceptive precautions during the trial and for 6 months following the last dose of study drug. * Females of child bearing potential must have had a negative serum pregnancy test less than or equal to 7 days prior to the first dose of study drug. * Have a serum albumin level greater than equal to 3.0 grams/deciliter (g/L), less than or equal to 72 hour prior to dosing with LY573636-sodium. Exclusion Criteria: * Have received treatment with a drug that has not received regulatory approval for any indication within 14 or 21 days of the initial dose of study drug for a non-myelosuppressive or myelosuppressive agent, respectively. * Participants with myeloproliferative disorders (for example, chronic myeloid leukemia (CML), polycythemia vera and primary myelofibrosis) other than essential thrombocythemia. * Have received an autologous or allogenic stem cell transplant within 75 days of the initial dose of study drug for the dose escalation phase or within 60 days of the initial dose of study drug for the dose confirmation phase. Recipients of an allogeneic stem cell transplant must have discontinued immunosuppressive therapy at least 24 hours before study drug administration with no more than Grade 1 acute graft-versus-host disease. * Have previously completed or withdrawn from this study or any other study investigating LY573636 sodium. * Have serious preexisting medical conditions that in the opinion of the investigator would preclude participation in this study. * Have serious concomitant disorders, including active bacterial, fungal, or viral infection, incompatible with the study. * Have a second primary malignancy that could affect interpretation of results. * Have a known coagulopathy or bleeding disorder, other than leukemic related thrombocytopenia. Participants with severe or life-threatening bleeding refractory to platelet transfusions are also excluded from this study. * Major surgery within 4 weeks of study enrollment. * Are receiving warfarin (Coumadin). * Females who are pregnant or breast feeding. * Have known positive results of human immunodeficiency virus (HIV), hepatitis B surface antigen (HBSAg) or hepatitis C antibodies (HCAb). * Have received treatment within 28 days of the initial dose of study drug with an experimental agent for noncancerous indications that has not received regulatory approval for any indication. * Participants receiving amiodarone, quinidine, propofol, or clozapine. * Participants receiving treatment with strong or moderate inhibitors of cytochrome P450 (CYP)2C19, including proton-pump inhibitors (PPIs). Esomeprazole or pantoprazole are allowed if not administered within 72 hours before or after LY573636 administration